Has "deep vs. wide" been resolved?
I am not sure what you are really looking for but I leave here this paper here, where some intuition into that direction is provided. This paper compares the performance of a deep learning model scaling in 3 dimensions: resolution, width and depth. As depicted in their definition:

If you go to section 3.2 you will see how scaling the different dimensions independently (resolution, width and depth) affects performance and how by performing a compound scaling the performance of the model is maximized (so there is a close relation). It is a very thorough ablation study. For me this was the paper where I understood how these Width, Depth and Resolution parameters come together.
Rethinking Model Scaling for Convolutional Neural Network: https://arxiv.org/abs/1905.11946